The Securities and Exchange Commission adopted a new set of disclosure rules for hedge funds, private equity funds and other private money managers Wednesday, but it backed off on several of the tougher requirements it had originally proposed.

The agency also exempted many firms from the new rules, saying they will apply only to those with at least $150 million under management.

SEC Chairman Mary Schapiro said the agency was taking heed of responses to a draft of the rules issued this year. Members of the financial industry had protested that the SEC’s proposal would have imposed unreasonable costs and burdens. Their objections carried special weight because a federal appeals court recently overturned a different SEC initiative on the grounds that the agency paid too little attention to corporate concerns and did not adequately assess the costs.

The requirements adopted Tuesday are part of the government’s response to the financial meltdown of 2008. Money managers will be required to file confidential reports with regulators to help them assess potential risks to the financial system and take steps to avert another crisis.

The filings will present a broad profile of their investment business, including strategies, reliance on debt and exposure to other firms.

To reduce the burden on money managers, the SEC abandoned a plan to require them to certify the filings under penalty of perjury. It agreed that they can use their own methodologies instead of a standardized approach to compute certain measurements in the reports. It gave firms more time to file the reports, and for managers of private equity funds, it reduced the frequency of the filings from quarterly to annually.

The rules require more information from firms that manage larger amounts of money, and more from managers of big hedge funds than from managers of big private equity funds.

The reports are meant to inform a new federal overseer, the Financial Stability Oversight Council.

Schapiro said that the agency concluded that private equity funds --which typically buy publicly traded companies, take them private and try to improve their performance before selling shares to the public again — pose less risk to the financial system.

The SEC is exempting the smaller money managers from the filing requirement because they have minimal impact on the government’s assessment of systemic risks, Schapiro said.

Firms covered by the new requirements would still represent a large majority of private funds’ assets under management, Schapiro said.